A room 5 M long and 4 m wide is surrounded by a wonder if the verandah occupies an area of 22 metre square find the width of the verandah
IS THIS REALLY THE CORRECT ANSWER???
IS THIS REALLY THE CORRECT ANSWER??? AND WHAT IS ^ THIS HERE ???
Width so you have to substitute X=1 into 4+2(1)=6
Therefore, the width of the verandah is 6m
To find the width of the verandah, we need to subtract the area of the room from the total area of the room along with the verandah.
Given that the room is 5 meters long and 4 meters wide, the area of the room is calculated by multiplying the length and width:
Area of the room = Length × Width
= 5 m × 4 m
= 20 sq m
Now, to find the width of the verandah, we subtract the area of the room from the total area (including the verandah) which is given as 22 square meters:
Width of the verandah = Total area - Area of the room
= 22 sq m - 20 sq m
= 2 sq m
Therefore, the width of the verandah is 2 meters.
The figure can be imagined as a smaller rectangle (the room) inside a larger rectangle (room plus verandah).
Area of veranda = Area of outer rectangle - Area of room
If you draw the figure, you'll see:
Length of outer rec. = (5+2x)
Width of outer rec. = (4+2x)
Length of room = 5
Width of room = 4
Where, x = width of the verandah
Area of veranda = Area of outer rectangle - Area of room
=> 22 = (5+2x)(4+2x) - 5*4
=> 22 = 8x + 10x + 4x^2
=> 2x^2 + 9x - 11 = 0
=> (2x+11)(x-1) = 0
=> x = 1, x = -11/2
Since the width cannot be negative, x = 1 meter
let width be x
length=5+x+x=5+2x
Width =4+x+x=4+2x
area=42m^2
so, (5+2x)x(4+2x)=42
(5x4)+(2x*2x)=42
2x*2x=42-(5x4)
2x*2x=22
x*x=22/(2x2)
x^2=5.5
x=5.5-3.5
x=1
THANK YOU !!!!!!!!!!!!!!!!!!..............
length = 5 + 2 w
width = 4 + 2 w
area = 22 = (2w+5)(2w+4) - 20
solve quadratic for w
22 = 4w^2 + 18w + 20 - 20
4 w^2 + 18 w - 22 = 0
2 w^2 + 9 w - 11 = 0
(2w+11)(w-1) = 0
w = 1